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Bureau of Mines Information Circular/1981 




Borehole Shear Tester: 
Equipment and Technique 

By Khamis Y. Haramy 




UNITED STATES DEPARTMENT OF THE INTERIOR 



y. 



J . 



Information Circular 8867 



Borehole Shear Tester: 
Equipment and Technique 

By Khamis Y. Haramy 




UNITED STATES DEPARTMENT OF THE INTERIOR 
James G. Watt, Secretary 

BUREAU OF MINES 
Robert C. Horton, Director 



CJh 



As the Nation's [X'incipal conservation agency, the Department of the Interior 
has responsibility for most of our nationally owned public lands and natural 
resources. This includes fostering the wisest use of our land and water re- 
sources, protecting our fish and wildlife, preserving the environmental and 
cultural values of our national parks and historical places, and providing for 
the enjoyment of life through outdoor recreation. The Department assesses 
our energy and mineral resources and works to assure that their development is 
in the best interests of all our people. The Department also has a major re- 
sponsibility for American Indian reservation communities and for people who 
live in Island Territories under U.S. administration. 






This publication has been cataloged as follows: 



Haramy, Khamis Y 

Borehole shear tester: equipment and technique. 

(Bureau of Mines information circular ; 8867) 

Supt. of Docs, no.: I 28.27:8867. 

1. Rocks— Testing— Equipment and supplies. 2. Shear (Mechanics)— 
Measurement. I. Title. II. Scries: Information circular (United States. 
Bureau of Mines) ; 8867. 



TN295.U4 [TA706.51 622s [624.r5132'0287l 81-607101 AACR2 



Hi 



CONTENTS 

Page 

Abstract 1 

Introduction 1 

Using the borehole shear tester 2 

Limitations 2 

Test hole specifications 2 

BST components 2 

BST assembly 7 

Procedure 8 

Cleaning the BST 8 

Data and calculations 15 

Bibliography 18 

Appendix— Seating pressure calculation for coal 19 

ILLUSTRATIONS 

1. Borehole shear tester components 3 

2. Closeup view of the t>orehole shear tester head 4 

3. Pulling assembly including hollow jack, half-nut, clamp, and dial gage 5 

4. Closeup view of the console 6 

5. Schematic of BST in the hole 7 

6. BST assembly, step 1 9 

7. BST assembly, step 2 9 

8. BST assembly, steps 3 and 4 10 

9. BST assembly, steps 5 and 6 10 

10. BST assembly, step 7 11 

11. BST assembly, step 8a 11 

12. BST assembly, step 8b 12 

13. BST assembly, step 8c-1 12 

14. BST assembly, step 8c-2 13 

15. BST assembly, step 8c-3 13 

16. BST assembly, step 8c-4 14 

17. BST assembly, step 9 14 

18. Normal stress calibration curve 17 

19. Shear stress calibration curve '. 17 

20. Example of BST plot 18 

A-1. Angle of plate inclination 19 



TABLES 

1. Types of shear plates available for various rock types 2 

2. Sample BST data sheet 15 

3. Completed BST data sheet 16 

4. Weights of BST components 18 



BOREHOLE SHEAR TESTER: 
EQUIPMENT AND TECHNIQUE 

By Khamis Y. Haramy^ 



ABSTRACT 



This Bureau of Mines paper describes the use of the borehole shear tester (BST) in 
mines. Assembly and procedure sections explain how the equipment is assembled and 
used properly. Schematics of the BST, limitations, test hole specifications, data record- 
ing, and calculations are all explained briefly, and an example of the data collecting and 
calculations is given to assist understanding. 



INTRODUCTION 



The borehole shear tester (BST) was developed by Dr. Richard L. Handy of Iowa 
State University in 1976 under Bureau of Mines Contract G0144021. The purpose of the 
work was to obtain a device for rapid, in situ measurement of rock shearing strength 
as a function of the normal stress acting on the plane of failure. The device is light in 
weight, mechanically simple, and easily transported. It is sufficiently durable to with- 
stand repeated use in adverse environmental conditions and can be used in the rib, 
roof, or floor of the mine. It requires an NX-size borehole. 

The data obtained from BST tests support well-known theories such as Mohr's 
theory of failure. This theory is based on a relationship between shearing stresses and 
normal stress at every point within the specimen body. The Coloumb theory, which is 
considered to be a special case of Mohr's theory, and the 1921 Griffith theory, which 
deals with material failure on a microscopic basis, are also supported by the BST 
results. 

Owing to the difficulty in obtaining large samples of coal and rock for laboratory 
testing and the bias that is introduced in large samples, the borehole shear tester 
promises to be of significant value to the mining engineer and researcher in determin- 
ing physical properties of in situ rock formations. 



'Mining engineer, Denver Research Center, Bureau of Mines, Denver, Colo. 



USING THE BOREHOLE SHEAR TESTER 



The BST is a device for making in situ tests to determine 
the shear strength of coal and rock using a 76-mm- 
diameter borehole (NX-size) up to 12 m long determines 
the shear strength as a function of the normal stress act- 
ing on a plane of failure. 



LIMITATIONS 

1. Do not use the BST in unsupported roof rock or 
within 1 foot of the borehole collar because it may cause 
spalling and buckling. 

2. Do not exceed a shearing stress of 6,500 psig. 

3. Do not fully extend the shear plates unless the BST 
body is in place inside the borehole. 

4. Use the right type of shear plates depending on the 
type of rock tested, as described in table 1. 



TABLE 1.— Types of shear plates available for various rock 
types 



Type 
desig- 
nation 


Configur- 
ation 


Tooth 

spacing, 

inch 


Number 

of 

teeth 


Tooth 

depth, 

inch 


Shear 

area per 

plate, 

sq in 


Remarks 


steel . . . 

Carbide 
insert. 


Flat full 
wedge. 

. . do . . 


0.4 
.8 


3 
2 


0.040 
.040 


0.8 
.7 


Used for 
softer 
rocks only. 

Used for 
coal and 
all other 
rocks.' 



'The upper limit of rock strength has not been decided. However, the 
device has been used in hard rock such as granite. 



TEST HOLE SPECIFICATIONS 

1. Diameter of test hole should be 76 mm (NX-size). 

2. Length of test hole should not be less than 1 meter. 

3. Hole should be dry to prevent rock dust penetrating 
behind the shear plates and thus preventing their free rota- 
tion. If water exists, the shear head swivel should be cov- 
ered with a heavy grease. 

4. Hole must be freshly drilled and clear of dust and 
cuttings, especially in rapidly deteriorating material such 
as coal and shale. 

5. Drilling may be done by diamond bit, pneumatic per- 
cussion drill, or others, provided the borehole is smooth, 
straight, and free of ridges. 

BST COMPONENTS 

The unassembled BST components are shown in figure 
1. 



Shear Head (fig. 2) 



1 . Two shear plates, each with two or three teeth which 
penetrate into ttie rock when normal pressure is applied, 
are mounted at the end of a double-acting hydraulic cylin- 
der. The plates are fixed in place and linked to individual 
push plates, which apply the normal force. Two types of 
shear plates are available for use with different ranges of 
rock strength (table 1). The steel plates are adequate for 
coal and softer rocks. If the teeth chip or wear, the carbide 
insert shoes should be used. 

2. The two push plates are connected to a locking 
mechanism and stay parallel during initial shear head 
expansion. 

3. Two short hydraulic hoses of different lengths are 
provided, which connect onto the BST body. One is used 
for shear plates expansion, the other for retraction. 

Pulling Assembly (fig. 3) 

1. A 12-ton center hole, hydraulic jack fits over thd 
threaded pull rod for pulling. 

2. An adjustable tripod is used to assure axial aiine* 
ment of jack and threaded rod. 

3. Jack base plate. 

4. A lock grip half-nut clamp provides a quick-acting 
stop nut on the threaded rod. 

5. A dial gage reads displacement of BST in the hole, if 
required. 

Console (fig. 4) 

1. Hand pump. 

2. Lever-type pump valve for "open-close" operating 
modes. 

3. Normal pressure valve and gage to read the applied 
pressure for normal forces against the shear plates. 

4. Shear pressure valve and gage to read the applied 
pressure for shearing forces between the shear plates and 
the rock. 

5. Manifold valve (expand-neutral-retract) used for the 
expansion and retraction of the shear plates. 

6. Three hydraulic ports (shear, retract, and normal)- 
onto which the hydraulic hoses connect. 

7. Two unmarked terminals for possible addition of 
shear and normal pressure transducers. (Otherwise these 
are left capped.) 

8. An aluminum case to protect the console. 

Miscellaneous 

Other BST assembly components include hydraulic ex- 
tension lines, threaded rods, RW adapters, and RW-size 
rods in 5-foot sections. Figure 5 shows a schematic of the 
BST and the way it should appear when placed in the hole. 




■m 



A. Console 

B. Hydraulic hoses 

C. Shear head (BST body) 

D. RW rod connector 

E. Half-nut clamp 

F. RW rod adapters 



G. Adjustable tripod 

H. RW rod 

I. Threaded rod 

J. Jack base plate 

K. Dial gage 

L. Hollow jack 



FIGURE 1.— Borehole shear tester components. 




FIGURE 2.— Cioseup view of the borehole shear tester head. 




Adjustable tripod"' , 

Jack base plate'' 



FIGURE 3.— Pulling assembly including hollow jack, half-nut, clamp and dial gage. 




FIGURE 4.— Closeup view of the console. 




Threaded rod — ~. 
Half-nut clamp 



Hollow jack 





^-Olal gage 



-Tripod 

^Jack baie plate 



Shear plates- « 



• ' •••■.-.•/ hqsj connector 



NX hole 



^>--BST body 



FIGURE 5.— Schematic of the BST in the hole. 



BST ASSEMBLY 

In assembling the borehole shear tester, refer to the se- 
quence of photographs 6 through 17 to help understand 
each step In the process. At least a 12-Inch pipe wrench, 
several screwdrivers, an 8-inch crescent wrench, shear 
plates, and hydraulic fluid are tools needed for the BST 
setup. 

1. Screw the RW rod adapter into the end of the BST 
body. This adapter adapts the thread in the BST body to 
the RW rod thread (fig. 6). 

2. Couple the hydraulic extension hoses to the hoses 
attached to the BST body (fig. 7). 

3. Mark the extension hose that is connected to the 
shorter hose from the BST body (fig. 8). (The BST has a 
long hose section and a short hose section attached to it.) 

4. Attach the RW rods in 5-foot sections to the rod 
adapter (fig. 8). 

5. Place the BST body in the hole with the shear plates 
at a known orientation, such as N-S or E-W, and a known 
depth (fig. 9). Record both orientation and depth on the 
data sheet. 

6. When the BST body is at the required depth, attach 
another RW adapter, to the RW rod (fig. 9). The reason RW 
rods are used is that they are much stiffer than threaded 
rods, which eliminates bending or stretching while the 
BST Is under shearing load. 

7. Screw in a 3-foot threaded bar to the RW adapter at- 
tached to the end of the RW drill rod (fig. 10). 

8. Mount the pulling assembly at the hole collar as 
follows: 



a. Place the jack base plate over the threaded bar 
and the hoses at the collar of the hole. Allow the hoses 
and the threaded bar to pass through the slot in the plate 
(fig. 11). 

b. Place the tripod with the adjustable screws 
against the jack base plate (fig. 12). These screws are used 
to aline the jack along the centerline of the hole. 

c. Slide the hollow jack over the threaded bar and 
against the tripod (fig. 13). Hold it in place, and after 
pushing everything tight together, secure the visegrip-type, 
half-nut clamp on the threaded bar tight behind the jack 
(fig. 14). The pulling assembly should look like figure 15 
before testing begins. The dial gage, shown in figures 13- 
16, is included in the assembly only if axial displacements 
of the BST are to be measured, see "Procedure" section. 



Caution:— \i the testing is in a vertical hole, the BST 
pulling rods and tripod assembly should be held in the 
center of the hole at the collar at all times until the normal 
seating pressure is applied. It is recommended that, for 
safety purposes, a safety chain and rod hook be used to 
hold the assembly in the vertical hole (fig. 16). 



9. Connect the hydraulic hoses to connectors, which 
are in the upper right-hand corner of the console (fig. 17), 
as follows: 

a. The marked hose (from step 3 of this section) to 
the port on console marked Normal. 

b. The other hose from the BST body to the port on 
console marked Retract. 

c. The hose from the jack to the port on console 
marked Shear. 



PROCEDURE 

The following procedure is for the BST in a vertical up- 
ward hole. In a downward vertical hole, the procedure is 
similar, except that when placing the BST body in the bore- 
hole, one should restrain it or it may be lost in the hole. 
Remember to record the orientation and depth of the shear 
plates before every test. 

1. Assemble the BST body, snap hoses on, connect 
rods, and place it in the hole as mentioned in the previous 
section, steps 1 through 7 and steps 9a and 9b. 

2. Place the pump valve and the valve labeled "shear" 
on CLOSE. 

3. Open the normal valve, and place the manifold valve 
on NORMAL EXPAND. 

4. Pump up normal gage pressure to a certain level 
which depends on rock type as follows: 

400 psig. . . Soft rock. 
1,600 psig. . . Medium rock. 
3,200 psig. . . Hard rock. 

Enough seating pressure must be exerted to achieve full 
penetration of the teeth into the rock or coal prior to the 
test, to insure that the teeth will shear off a coupon of rock 
or coal and not simply scrape the surface. Excessive dis- 
placement during the test or low apparent shear strength 
may indicate the need to apply a higher seating pressure. 
The seating pressures given above are typical and may be 
used as a guide. The appendix gives more details on seat- 
ing pressure calculations. 

5. CLOSE normal valve. 

6. Wait 5 minutes for the teeth on the shear head to 
penetrate into the rock. Remember to keep holding the 
BST in the hole until normal pressure is applied. 

7. Mount pulling assembly at the borehole collar as ex- 
plained in steps 8a through 8c in the previous section. 

8. Snap on the jack hose according to step 9c. 

9. Adjust the dial gage for a zero reading and record it 
on the data sheet if BST axial displacements are to be 
made. 

10. OPEN normal valve. 

11. Readjust normal pressure to the chosen setting 
pressure (if any change in pressure has occurred) by either 



pumping (to increase pressure) or opening pump valve 
slowly (to reduce pressure). 

12. CLOSE normal valve. 

13. OPEN shear valve. 

14. Pump at a slow rate until shear gage reads 100 psig, 
then record the following data on the data sheet (see ex- 
ample in appendix): 



Normal pressure 
Shear pressure . 
Displacement . . 



From normal gage on console. 
From shear gage on console. 
From dial gage if desired. 



15. Pump the shear pressure in steps to 200 psig, 400 
psig, 600 psig, and so on until the peak shear has been de- 
termined. Record shear pressure and displacement for 
each pressure. If the pulling rod bends as the shear 
pressure is increased, the load should be released and the 
tripod adjusted so that the pulling action is parallel to the 
axis of the hole; otherwise the displacement measure- 
ments will be meaningless and the pulling rods may be 
damaged. 

16. Continue to pump until shearing pressure changes 
are relatively slow or a predetermined maximum displace- 
ment is reached. 

17. Upon each completion of each test, OPEN pump 
valve, CLOSE shear valve, OPEN normal valve, and switch 
manifold valve to retract. 

1 8. Before removing BST from hole, CLOSE pump valve, 
CLOSE shear valve, keep normal valve OPEN, and pump 
until the shear plates retract and the BST head apparatus 
pulls loose from the hole. 

19. For the next sequential test, reinsert the device in 
the hole either rotated 45° at the same depth, or at a differ- 
ent depth. Repeat all above procedures. 

A/ofe.— When the BST is used in harder rocks, the shear 
plate teeth may wear enough during a series of tests to 
begin to affect the results. The effect of this wear should 
be distributed over the length of a test hole by randomizing 
the depths and orientations of the shear tests. 



CLEANING THE BST 

After every test, clean off shear plates and make sure 
they swivel freely. After the completion of all testing, clean 
the BST body very well and lubricate it by using a WD-40 
lubricant spray (or equivalent) to prevent rusting. 




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15 



DATA AND CALCULATION 



A blank data sheet for the borehole shear tester data ap- 
pears as table 2; each sheet should be filled in completely 
as shown in table 3, including the name and location of 
the mine, the type of rock tested, the hole specifications, 
the date of testing, and the name of the person(s) doing 
the testing. 

Every BST has two calibration curves, similar to the 
ones shown in figures 18 and 19. One is a normal stress 
calibration curve; the other is a shear stress calibration 
cun/e. The normal gage pressure Pn and the shear gage 
pressure Ps (in psig) are read from the normal and shear 
gages respectively on the console. The normal stress on 
and the shear stress Ts (in psi) are calculated from for- 
mulas such as the following: 

Normal stress (on) = 2.604 Pn- 85.135 (1) 

Shear stress (Ts) = 1 .744 Pn - 81 .035 (2) 

Formulas 1 and 2 were obtained from the calibration 
curves. Both curves have a small negative intercept. (One 
may also use the curves in figures 18 and 19 to obtain on 
and Ts). 

The calculated normal stress on is plotted on the X-axis 
versus the calculated shear stress Ts on the Y-axis on 
linear-linear graph paper. The best-fitting straight line is 
drawn through the plotted points. The cohesion (in psi) for 
a particular rock is indicated by the intercept of this fitted 
line with the Y-axis. Provided that the scales are the same, 
the angle of internal friction <t> is the angle between the 
X-axis and the plotted line as shown in figure 20. The angle 



of internal friction can also be calculated as the arc tan- 
gent of the slope of the plotted line. 

<|> = arc tan p< 

where ^ = the slope of the line (coefficient of friction). 

The calculation of the BST tests made in a Utah coal 
mine given in table 3 should help clarify the calculations. 

A Bureau of Mines computer program can be used to 
analyze the BST data; a copy may be obtained from the 
author of this paper at the Bureau of Mines, Denver, Colo. 

In calculating the shear stress, the weight of the BST 
assembly (see table 4) should be taken into consideration 
as follows: 

1. In an uphole, the shear stress caused by the weight 
of the BST body and the hoses used in the hole. The 
weights of the RW-size drill rods, threaded rods, plates and 
tripod, and hollow jack should all be added to the maxi- 
mum shearing force required. If a dial gage is used, its 
weight should be added. 

2. In a downhole, the shear stress caused by the weight 
of the BST body, hoses used in the hole, and RW rods 
should be subtracted from the maximum shearing force 
required. 

3. In a horizontal hole, the shear stress caused by the 
weight of the BST assembly has a very small effect. There- 
fore it does not have to be included in the shearing force 
calculations, and no adjustments are required. 



Mine 

Type of rock 
Hole No 



Roof 



.Hole location. 



TABLE 2.— Sample BST data sheet 

DATA SHEET FOR BOREHOLE SHEAR TESTER 

Date 

Tested by 

Floor 

Hole depth 



Test 


Normal 


Shear 


Orientation 
of teeth 


Depth 
into hole 


Displacement 


Po 


On 


Ps 


Ts 



































































































































































































































































































'n = Normal gage pressure (psig) 
On = Normal stress (psi) (calculated). 
Pn = Maximum shearing gage pressure. 
Ts = Shearing stress (psi) (calculated). 



16 



TABLE 3.— Completed BST data sheet 

DATA SHEET FOR BOREHOLE SHEAR TESTER 
Date 



OCTOBER 1, 1980 



Mine 

Type of rock 

Hole No. W-25 



COAL MINE "X", UTAH 



COAL 



SANDSTONE 



Hole location 



Roof 

HOLE IN ROOF, CROSSCUT 
#25, 3d Rt. 



Tested by 
Floor 
Hole depth 



HARAMY AND DeWAELE 



30'(NX-HOLE) 



Test 


Normal 


Shear 


Orientation 
of teeth 


Depth* 
into hole 


Displacement 


Pn 


On 


Ps 


Ts 


1 


1000 


2392 


1350 


1841 


NS 


12'5" + H** 


— — 


2 


1250 


2990 


1700 


2318 


NS 


107.5" + H 


— — 








250 


ZERO READING 
ON DIAL GAGE = 6.0 




5.95 0.05 








500 




5.61 0.39 








750 




5.25 0.75 








1000 




4.85 1.15 








1250 








4.20 1.80 








1500 








3.56 2.44 








1700 


PEAK 




2.43 3.57 


3 


1500 


3588 


1760 


2400 


NS 


8'4.5' + H 


— — 








250 








5.00 0.00 








500 








4.90 0.10 








750 


ZERO DISPL. = 5.0 




4.79 0.21 








1000 




4.44 0.56 








1250 








2.77 2.23 








1500 








.16 4.84 








1760 


PEAK 




- - 


4 


1750 


4186 


2200 


3000 


EW 


8'11" + H 


— — 








250 








5.80 0.20 








500 


ZERO DISP = 6.0 




5.27 0.73 








750 




5.09 0.91 








1000 








4.84 1.16 








1250 








4.60 1.40 








1500 








4.21 1.79 








1750 








3.68 2.32 








2000 








2.88 3.12 








2200 


PEAK 




1.30 4.70 


5 


2000 


4784 


2350 


3205 


EW 


11'0" + H 


— — 








500 








6.55 0.45 








750 


ZERO DISPL. = 7.0 




6.14 0.86 








1000 




5.72 1.23 








1250 








5.40 1.60 








1500 








5.09 1.91 








1750 








4.70 2.30 


5 






2000 








3.50 3.50 








2250 








2.00 5.00 








2350 








1.92 4.08 


6 


2250 


5380 


3010 


4106 




12'6" + H 


- - 








500 








7.09 0.91 








1000 








6.05 1.95 








1500 








5.49 2.51 








2000 








4.90 3.10 








2500 








3.92 4.08 








3000 








2.15 








3010 








- - 



'Distance from collar ot borenoie to the 
center of loading plates 
•H = Length of BST head 1.5' 



Pn = Normal gage pressure (psig) 
On = Normal stress (psi) (calculated) 



Ps = Maximum shearing gage pressure 
Ts = Shearing stress (psi) (calculated) 



17 



14,000 



12,000 - 



1 0,000 - 



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2.000 3,000 

NORMAL GAGE READING (Pn\psig 

FIGURE 18.— Normal stress calibration curve. 



4.000 



5,000 



10.000 



8.000 



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6,000 


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2,000 



Ts= 1.744 P5-8I.O35 
r =0.9998(coeff. of correlation) 
n= 18 (number of tesfs) 

BST serial number 1104 



-L 



1,000 2P00 3^P00 

SHEAR GAGE READING (Pjj.pslg 

FIGURE 19.— Shear stress calibration curve. 



4p00 



5.000 



18 



4.000 



3,000 





I 1 r 

Mine; Utah cool mine 




Type of rock : Sondstone 




Dote of test : Oct. 1, 1980 


- 


Tested by Haramy and DeWoele 



to 
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►- 

V) 

a: 

< 

UJ 
X 
CO 



1,000 



.NOV* 



yKO 



»xv< 



:s 



^>-Ts = 800 + o-n ton 2 6.56* 



Slope = 0.5 

i> (angle of internal friction) = 26.56° 



SO 

ooo 
o 



1,000 



J. 



X 



2,000 3,000 4,000 

NORMAL STRESS {a-n),psi 

FIGURE 20.— Example of BST plot. 



X 



5,000 



6,000 



TABLE 4.— Weights of BST components 



Component 



RW rod 

BST body and 2 attached short hoses . 

Hydraulic hoses and fluid 

Tripod and base plate 

Dial gage 

Threaded rods 

Hollow jack 

Half-nut clamp 



Weight 



1.8 'bf/ft 
9.5 lt>, 
0.1 lb/ft 
7.0 1b 
1.0 1b 
1.5 lb/ft 
11.01b 
.81b 



'Stress : 



weight 



2 (cross-sectional area of plates) 



Stress' 



0.45 psi/ft 
2.375 psi 
0.025 psi/ft 
1.750 psi 
0.250 psi 
0.375 psi/ft 
2.750 psi/ft 
0.200 psi 



NOTE.— This table also allows the operator to decide whether a winch is 
needed to hold the BST assembly as opposed to the operator handling 
the weight. 



BIBLIOGRAPHY 



1. Handy, R. L, J. M. Pitt, L. E. Engle, and D. E. Klockow. Rock 
Borehole Shear Test. Proc. 17th U.S. Symp. on Rock Mech., 
Snowbird, Utah, Aug. 25-27, 1976, pp. 4B6-1-4B6-11. 

2. Panek, L A. Criterion of Failure for Design of Rock Mass 
Structures as Determined by Borehole Shear Tests. Proc. 4th 
Cong., Internat. Soc. for Rock Mechanics, Montreux, Switzerland, 
Sept. 2-8, 1979, v. 2, pp. 509-515. 



19 



APPENDIX— SEATING PRESSURE CALCULATIONS FOR COAL 



The coefficient of sliding friction can be calculated as 
follows: 

/i = tan/? 

where ^ = coefficient of friction 

and p = angle of friction between the shear 

plates and the material being 
tested. 

In laboratory testing by the Bureau, the coefficient of 
friction between coal and steel was found to be 0.3 ± 0.04. 
From equation 1 

p = arc tan (0.3) = 16.7°. 

The minimum normal stress to cause material failure 
can be calculated using the following formula: 

^o < tan(0 + /3)-tan<fr 
On 

where Co = materials cohesion, 

On = normal stress, 
6 = angle of plate inclination shown in 

figure A-1, 
p = angle of friction between steel 
plates and rock tested, 
and <!• = angle of internal friction of the 

material. 




FIGURE A-1.— Angle of plate inclination. 

Substituting in equation 2 

= 60° Fixed, 

•t- = 60" Highest for coal, 

and p = 16.7° from equation 1 

Thus, for coal with Co = 1,000 psi, the minimum o„ to 
cause material failure rather than slippage is 

Co 

< 2.5 

On 
1,000 

On > > 400 psi. 

2.5 

The normal stress will vary depending on Cg and ^ of 
coal. This method of estimating o„ is a good approxima- 
tion and may be used for any type of rock. 



*U.S. Government Printing Office : 1982 -364-576/7289 



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